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    <title>lqg_ltr</title>
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    <center>Scilab Function</center>
    <div align="right">Last update : 13/01/2005</div>
    <p>
      <b>lqg_ltr</b> -  LQG with loop transform recovery</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>[kf,kc]=lqg_ltr(sl,mu,ro)  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>sl</b>
        </tt>: linear system in state-space form (<tt>
          <b>syslin</b>
        </tt> list)</li>
      <li>
        <tt>
          <b>mu,ro</b>
        </tt>:  real positive numbers chosen ``small enough''</li>
      <li>
        <tt>
          <b>kf,kc</b>
        </tt>: controller and observer Kalman gains.</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
    returns the Kalman gains for:</p>
    <pre>

           x = a*x + b*u + l*w1   
  (sl)
           y = c*x + mu*I*w2

           z = h*x
   
    </pre>
    <p>
    Cost function:</p>
    <pre>
      /+oo
                   |
          J    = E(| [z(t)'*z(t) + ro^2*u(t)'*u(t)]dt)
           lqg     |
                   / 0
    </pre>
    <p>
    The lqg/ltr approach looks for <tt>
        <b>L,mu,H,ro</b>
      </tt> such that:
    J(lqg) = J(freq) where</p>
    <pre>

                  /+oo        *  *           *
          J    =  | tr[S  W  W  S ] + tr[T  T]dw
           freq   |
                  /0
    </pre>
    <p>
    and</p>
    <pre>

 S = (I + G*K)^(-1)  
 T = G*K*(I+G*K)^(-1)
   
    </pre>
    <h3>
      <font color="blue">See Also</font>
    </h3>
    <p>
      <a href="../elementary/syslin.htm">
        <tt>
          <b>syslin</b>
        </tt>
      </a>,&nbsp;&nbsp;</p>
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